It describes Turing as "one of the greatest heroes of the 20th century" for helping to crack the Enigma code and says he was "pivotal in the development of modern computers".

The letter continues: "The apology and pardon of Alan Turing are to be welcomed but ignores over 49,000 men who were convicted under the same law, many of whom took their own lives.

"An estimated 15,000 men are believed to still be alive."

'Totally unjust'

Cumberbatch, who has been nominated for an Oscar for his portrayal of Turing, and The Imitation Game's director Morten Tyldum are also joined as signatories by Turing's great niece Rachel Barnes and Matthew Todd, editor of Attitude Magazine.

Ms Barnes told BBC News the royal pardon given to Turing was "fantastic for all of us because he was such a great man and did so much for this country."

"But we've always considered that it is totally unjust that only Alan was given a pardon," she said. "There were 50,000 other homosexuals who were convicted and not given a pardon. We would really like this to be put right now."

An estimated 15,000 of them are still alive, she added.

An online petition has also been launched at www.Pardon49k.org, with more than 60,000 having signed it so far.